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cosineEscapeTime =
Compile[{{c, _Complex}},
Block[{z = c, n = 2, escapeRadius = 10 \[Pi], maxIterations = 100},
While[And[Abs[z] <= escapeRadius, n < maxIterations],
z = Cos[z] + c; n++]; n]]
DensityPlot[
cosineEscapeTime[x + I y], {x, -2 \[Pi],
2 \[Pi]}, {y, -\[Pi], \[Pi]}, PlotPoints -> 250,
AspectRatio -> (1/2), ColorFunction -> "TemperatureMap"]